# Magnetic Dipoles

" There are some things so serious that you have to laugh at them"
Niels Bohr
• Shown below is a rectangular current loop sides a and b placed in a region of space with uniform magnetic field (B).

• Application of the expression for the force on a current carrying wire to the top and bottom sides of the rectangle leads to cancellation of forces as shown.
• The forces on the other two sides (length a) are also equal and opposite, as shown in (b) above, .  Although the net force in this case is zero, because the forces are not co-linear, there is a net torque on the current loop, given by

The magnitude of this torque is given by

where A = ab is the cross section area of the coil.
• The magnitude of the magnetic dipole moment of the loop with N turns is defined by,

μ is a vector quantity whose direction is perpendicular to the loop with a sense defined by (another) Right Hand Rule.
• With this definition of μ the torque on the current loop is given by

• Without proof, the potential energy of a magnetic dipole in an external magnetic field is given by

Note that the above expressions for the torque and potential energy of a magnetic dipole in an external magnetic field are identical in form to those obtained for an electric dipole in an external electric field.

and

I stayed up all night to see where the sun went.  Then it dawned on me.

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu